Page 84 - IJPS-10-4

International Journal of
Population Studies Migration and child mortality estimation

q() = ()() (I) before age x different from that of the actual population.
where () is the proportion of children dead among One is when the survey population differs from the actual
children ever born to women of age group i, and () is population, causing the functions () and () to differ

the translation scale factor based on the average parity from the functions () and (), respectively. The other
of women of age group i. Essentially, the Brass indirect source of error in the estimate of mortality occurs when the
method requires the application of a model fertility and model chosen does not match the actual study population,
child mortality pattern (United Nations, 1983). resulting in differences between the functions *() and
*(), and the functions () and (), respectively.
Using a theoretical model, Arthur & Stoto (1983),
demonstrated that despite the popularity of the Brass Now, suppose the model chosen for the estimation of
indirect method, child mortality estimates obtained using π () correctly represents the actual Population; but the
this method are prone to errors. The model consists of three () deviates by due to a deviation in the proportion of
populations: The actual population targeted to estimate children dead. Then, the differential estimate, (), caused
the child mortality rates, the survey population consisting by the deviation of the proportion of children dead,
of women selected for the interview, and the artificial (i), is given by Equation VI:
or model population chosen for the simulation of the
translation of the ratio k. In this model, the corresponding π () = [() ⁄ ∫ ()()] () (VI)
mortality rates associated with these populations and their In terms of proportional error, we have Equation VII
respective density functions representing the number π()/() = [/∫ ()()] = ()/() (VII)
of children (dead or alive) born to women of age are
summarized in Table 1. From Equation VII, we find that the proportional error
in the estimate is the same as the proportional error in .
Using the model functions, D() is given by Equation II:
In this study, we extend this concept by considering
() = ∫() () (II)
the error in child mortality estimates q() due to variation
and k is estimated by Equation III: in caused by migration. The Brass indirect method
= *() ⁄∫*()*() (III) assumes that the population whose child mortality rates
are being estimated is close to migration or that there
Then, the probability of dying between birth and age x, is no mortality difference among regions exchanging
denoted as π(), can be expressed as Equation IV: populations through migration (Schmertmann &

π () = [*() ⁄ ∫*()*()] ∫ () () (IV) Sawyer, 1996). However, the migration of women across
different geographical regions within a country is a
The estimate π () can be written as Equation V: common phenomenon. When migrant women provide
π () = [*()⁄∫*()*()] () (V) information about their deceased children at the time of
From Equation IV, there are two possible sources of the survey, they do not provide the geographical location
errors that can make the estimated probability of dying where the death occurred. During the analysis of child
mortality, the reported deceased children are assumed to
have died in the mother’s current place of residence. In
Table 1. Model functions for error analysis in indirect child this case, the deaths of children born to migrant women
mortality estimation that occurred before the mother migrated to the current
place of residence are misclassified by their geographical
Function Definitions
place of occurrence. If the migrating segment of the
q(x) Probability of dying between birth
and age x in the actual population women’s population has a different mortality regime
c(x) Density of children at age x of mothers from the recipient population, the child mortality
aged x in the actual population estimates for the recipient regions will be inaccurate.
q (x) Probability of dying before age x for This, in turn, affects the accuracy of the child mortality
s estimates in these regions. Several studies have also
children in the survey population
c (x) Density of children at age x in the pointed out the need to account for migration when
s computing sub-national child mortality rates (Bocquier
survey population at the time of survey
et al., 2011; Otieno Onyango et al., 2011; Schmertmann
q*(x) Probability of dying before age x in the model population
c*(x) Density of children at age x of & Sawyer, 1996).
mothers aged x in the model population In our study, we sought to determine whether there is
Note: Adopted from Arthur & Stoto (1983). any statistical impact on indirect child mortality estimates

Volume 10 Issue 4 (2024) 78 https://doi.org/10.36922/ijps.1837